Which of the following values are solutions to the inequality 5<7+5x
I.6II.−5III.−7
Answer
Multiple Choice Answers
NoneNone
I onlyI only
II onlyII only
III onlyIII only
I and III and II
I and IIII and III
II and IIIII and III
I, II and IIII, II and III
To solve the inequality 5<7+5x, we need to isolate the variable x.
Subtract 7 from both sides of the inequality:
5-7 < 7+5x-7
-2 < 5x
Divide both sides by 5 (keeping in mind that dividing by a negative number flips the inequality symbol):
-2/5 > x
So, x is greater than -2/5.
Now let's go through the answer choices to see which values satisfy this inequality:
I. 6: 6 is greater than -2/5, so it is a solution.
II. -5: -5 is not greater than -2/5, so it is not a solution.
III. -7: -7 is not greater than -2/5, so it is not a solution.
Therefore, the only value that is a solution to the inequality is I only.